Question

How do you write `w^2+18w+77` in factored form?

Answer 1

`color(blue)((w+7)(w+11)`is the factorised form of the expression.

Explanation:

`w^2+18w+77`

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like `aw^2 + bw + c`, we need to think of 2 numbers such that:

`N_1*N_2 = a*c = 1*77 =77`
AND
`N_1 +N_2 = b = 18`

After trying out a few numbers we get `N_1 = 7` and `N_2 =11`
`11*7 =77`, and `11+7= 18`

`w^2+18w+77 = w^2+11w +7w+77`

`w^2+11w +7w+77 = w(w+11) + 7(w+11)`

`=color(blue)((w+7)(w+11)`

Answer 2

Factor `w^2 + 18w + 77`

Ans: y = (w + 7)(w + 11)

Explanation:

I use the new AC Method (Socratic Search) that is simpler and that avoids the lengthy factoring by grouping.
y = w^2 + 18w + 77 = (w + p)(w + q).
The 2 numbers p and q have same sign. Compose factor pairs of 77.--> (1, 77)(7, 11). This sum is 18 = b. Then, p = 1 and q = 77.
Factored form y = (w + 7)(w + 11)